Not Another Swan

“Not another swan!”, groused John Smith, some 30 years after founding the British Origami Society. “[A]fter all, how many new swans do we really need?…Are there yet more fine horses still waiting to be brought into being?”

Did someone say, “Horse”? Hmm…. No. Today we are making a Swan. Sorry, John.

This swan does not inflate, I regret to report. It does not shake its wings when you pull its tail. But it will FLOAT—for long enough, anyway, till you fold another one. And you can teach it to a child.

Instructions (quick version): Make a stretched bird base, double-rabbit-ear the neck, sink a tail, make a head, upend bottom & tail. Q.E.D.


Saadya

Old and New

Horse

I won’t say this is my favorite model. They are all my favorites while I am working on them. But this Horse--I have been with her the longest, starting I think in 1993. Also I have a set of ideals, almost an ideology, for animal origami design, and this is the model that comes closest to embodying it.


1. It is from a square

2. It uses clean angle divisions (15, 22.5) for all major folds (and most minor ones)

3. The preferred angle basis is 15 degrees (which I happen to like)

4. It uses strict referencing till very late in the sequence

5. The referencing is not artificial, but natural (= few/no extra steps just to make references)

6. The number of folds, given what you get at the end, is small (about 40 for the basic, standing version)

7. For horses in its class, paper usage is highly efficient

8. A quite reasonable model is produced with no post-folding, but material enough is there so that an accomplished folder can sculpt it to his heart’s content

9. Different poses or expressions are possible, because many long limbs are independently repositionable without affecting the others (head, neck, mane, tail, legs to a small extent)

10. It is from a Base or ‘embryo’ that can be readily modified to yield other animals

11. No body lines appear on the model that aren’t there in reality, and all those on the real animal are on the model

12. It is closed-back

13. Long limbs are visually continued by body lines

14. It is a beautiful animal.



Shortcomings too may be listed:

1. It is mainly a ‘flat’ model, though it becomes three-dimensional fairly naturally owing to paper thicknesses. (Unlike, e.g., the Pigeons from earlier this month, which are 3D directly by the folds.)

2. Legs should be longer still, to allow proper hooves and more motion poses.

3. While it is ‘closed-backed’, it is ‘open-headed’

4. If done with duo-toned paper, the head comes out a different color, as do the inner sides of the legs. This may or may not be desirable.


As if to balance out these deficiencies: unexpectedly, a version can readily be made that is also an Action Model.


DESIGN HISTORY. Of the three poses shown, the Galloping variation is most recent and has been through only 2 revision cycles (a few evenings’ work) so can’t be called perfect even if it’s good enough to show . The Grazing pose is much older & has been through 3 or 4 revision cycles, the first of them very long ago; I’m not fully satisfied with it either. But the Standing pose, the oldest, has been through at least 7 cycles, beginning I believe in 1993, then set aside till 2004 when I came back to origami. (During which time standards had toughened--for instance ‘open-backed’ animals like this horse used to be suddenly had become 'inferior'). At this point I’m not sure I can improve on this model any further, but you never know.


TRIPARTATE DIVISIONS. The length of the side of the square is divided into three, and so are the main 90-degree angles. The first—the length-division—is pretty much arbitrary; you can vary it and still get a decent animal only it will have a somewhat longer or shorter body which may not be suitable for a horse. (In fact a more perfect Horse can be made with a slightly different division, but I can’t be bothered to establish a reference of "side x 0.31".) The division of the angle into three is more fundamental; for clean folding purposes your options are either 15 or 22.5 degrees, and I happen to like multiples of 15. --Among other reasons because it was less common in 1993 when I started, though it is famously used in David Brill’s fine Horse from an equilateral triangle.


NATURAL FOLDS. A fold sequence can use strict referencing, or it can use ‘judgment calls’ or bizarre fractions for references. The designer most famous for strict referencing is the wonderful Komatsu, and he is liable to devote a fifth or more of the steps in a sequence to establishing marks precisely on the square. (He too has a Horse, of course, and a noble beast it is.) This calls attention to the act of referencing, which is in part why Komatsu has the reputation he has; but it seems to me that a higher & tougher design ideal is to establish references without special moves dedicated to them, that is, to make active, form-creating moves and base each next move on references naturally left by previous ones. Referencing is then no less strict for all that it happens silently.


EMBRYO. I worked hardest here to develop a supple animal base, or what might be called an ‘embryo’, which can be turned into a Horse or into any number of different animals. (It really is like embryology: remember Von Baer’s Law, that organisms are more like each other the younger the stage you look at them, both within and across species.) I prefer to get to an embryo stage much sooner than some other designers do, because this speed is what gives you the flexibility to change poses (or species) if need be.


SCULPTING. I'm a reasonably good sculptor and will often tinker for hours with a ‘finished’ model to get it into the right pose or expression. As a model designer this theoretically puts me in conflict with those folders who want a model at the end of a fold-sequence to come out as close to finished as possible, with little or no post-folding. Actually the conflict is less than it might seem--and enters at a different location than may be thought. Like everyone else, I want a model to be as good as it possibly can be straight off the assembly line. But I also try to design in as much flexibility as possible, so that if tinkerers like me DO want to change things at the end, they will not be locked in by the structure of the model. Designing for maximum uniformity of result is a very interesting concept, but there is also such a thing as designing for maximum variability, and it is not necessarily less challenging.


CREASE PATTERN. Someone who never folds from crease patterns really has no business unleashing on the world a CP of any model of more than minimal complexity. Understanding and skill is needed, to know what to include & exclude. Nevertheless—I promised, so here it is. --A holiday gift: to you who like such things.

Added Dec. 2010: Diagrams for the standing & grazing poses now available in my book, "Sculptural Origami".

Sparrow

I gave in a little too easily a few posts ago to the claim that a bird base doesn’t conveniently allow a two-winged, split back without pre-placement of grafts, etc. Actually here, the desires of the origami designer to show what can be done with points come into conflict with nature’s aesthetics, since most of the time birds are standing around, their wings and tail really are conjoined in one streamlined, seamless unit. But supposing you do insist on showing wing-tips as points—it is not necessary to have them be fully independent. It’s enough to indicate the separation. And if so, a bird base is perfectly adequate to the task.

In fact now that I’ve been around the world, so to speak, with fancy bases and fancy variations to them, I keep coming back to simpler things. The traditional bases turn out to do the job better than the fancy ones! Here is that damn plain-vanilla Bird Base again. And this time I think I can illustrate the idea of continuous complexity directly with this model:

Basically, the moves are:

1. Bird base

2. Color reverse one face of the base

3. Rabbit-ear the other (colored) side around the paper’s squared-off center, while sticking a finger to open the pocket underneath

4. Color-reverse the head too--by loosening the paper almost all the way, making a shallow rabbit-ear, then closing the whole assembly again.


In diagrams here is where you would be in about 10 steps:


One could, in fact, stop hereabouts, or slightly afterward, and have a perfectly reasonable ‘childish’ model. Or perhaps one can think of this as an embryonic stage.

But even if you don’t stop, you should at least pause here, and let the purity and cleanliness of these surfaces and lines sink into your soul. The expanse of unmarked paper, held flat or curving, that shows paper for what it is; and the few long folds, where origami can be seen in its fundamentals. Whatever you do from this point on is going damage the purity of the form. --That may very well be necessary, but you’ll want to minimize the damage, and weigh the benefits of every choice against its cost. Anyone incapable of feeling pain at what about to be lost here will never be more than a technical folder.

To complexify, you might decide to point-split feet, split open a beak, cut the tail into virtual wings plus a tail, ornament the tail further, put feathers on the wings or whatnot. What should guide these choices? There’s a tendency, in today’s testosterone-driven origami, to do what’s technically more difficult, or at least more elaborate, so that you get these scales of complexity: if there are claws, then there must also to be an open beak, wings detached from the joint, etc. etc.

I humbly suggest that restraining one’s gonads here is the wiser course. In design it is generally asked what is the most you can make out of the material you have at hand. That makes perfect sense. But it can also be reasonable to ask, what is the least you can make of it, and still have something worthwhile. For the ratio of means to ends is what finally gets considered, not the absolute values of each. That is the rule for art in general; and for origami, which is all about the Something-from-Nothing, it is true all the more.


* * *

The Sparrow up top is my first experience folding at home with Origamido paper. Boy is it a pleasure! I wish I could afford it! It's what we'll all be folding with in the Origami Afterlife.

Let me wish Michael LaFosse and Richard Alexander a smooth transition to their new quarters in Honolulu. I was born in Boston, even if I don’t live there now, and as a native let me say: this departure is a real loss for the city and for the entire U.S. East Coast. Bon Voyage regardless.


Happy holidays everyone.





[Added 10.29.07]

Pigeon Frenzy

I’m not going to show you two week’s worth of experiments on the Fat Pigeon. My table is littered with bird carcasses, and my brains are in worse state because once I start I don’t stop and now two weeks are gone from my life. The problem, besides the wounded pride hinted at in the last entry, is that I foolishly listened to R. J. Lang two years ago in Barcelona, when he said ‘birds really ought to have their feet point-split’. I disagreed, but out of politeness conceded that “this was at least true for pigeons.” And here was my old Fat Pigeon, standing around pigeon-legged instead of pigeon-toed.

Unfortunately the most obvious way of solving this puts a nasty pleat at the edge of the paper; legs and claws can then be made as long as you like. Now, while I dislike box-pleating I am not opposed to it in principle, if the pleats are put to some artistic effect when the time comes. But here the pleated bulk ends up in the worst place, locked uselessly within wings and tail; and to tie up 20 or 30% of the square just so you can later pry apart some toenails—no, that I will not do. So far as I’m concerned you may as well start with a rectangle or cut the paper.



I have since come up with some more reasonable solutions, supposing feet must indeed be split. But let us first look a little more closely at this assumption, and what is behind it.

Birds have feet, no? So splitting toes is a way of making improved, more representationally-accurate origami—isn’t it?

Not necessarily. Google any picture of a robin or any other small bird. Half the time, do you even see the feet? Feet seem to be something of an embarrassment for bird aesthetics. That is: even male birds, which use flashy colors for their bodies and even sharper detailing on their heads—along with eye-catching profiles that may be egg-like or sinuous—even such birds, who are hardly ashamed of calling attention to themselves, use the universal language of crypsis when it comes to their feet. Feet and even legs on small birds are often thin, reedlike and brown, blending right in to the ground or twig they are perched upon. Sometimes they are knobby and ugly, in contrast to the gorgeousness up above, and in that way too slide attention off themselves.

In other words, a representation of feet may be accurate anatomically without being accurate visually. Drawing attention to them, to show that you are a moderately competent designer who knows how to split a point, is doing something that may be in conflict with what the bird is trying to do, and also with how a bird’s image lingers in the mind.

What, then, is driving the point-splitting of bird-feet in origami, if it isn't aesthetics? It seems to me there are two factors. First is that the older style, from early Yoshizawa, where feet were made by a simple (or a double) reverse fold, really is unsatisfactory in many cases. The bird ends up looking like it is wearing boots. Point-splitting here is a legitimate response to a problem, and is indeed an improvement if (a) you want a stable standing animal and (b) the bird’s feet are going to be looked at anyway. Of course you can also bite the bullet and leave the legs as one long point, or eliminate them altogether as LaFosse had the courage to do.

But a second factor is the current fashion of super-complex, hyper-technical origami, which regards it as an embarrassment if any long points are left anywhere unsplit. A pleasant illustration of this is provided in the Swan by Noboro Myagima, that appears in the AEP Convention Book 2005 (another ‘Barcelona bird’…). The folding sequence is 149 steps long. But at the end of these 149 steps, you do not end up with a Swan which is noticeably better than the ones you learned as a child, that took 10 or 15 steps. Myagima’s model does, however, have one advantage over those older, more modest ones: its feet are point-split. We may note that it holds this advantage over real-life swans too, which, alas, are stuck with merely webbed feet .


Getting back to the carnage from the last two weeks:

I took the Fat Pigeon [CP], a form almost 20 years old--a completely natural, lyrical, geometric sequence from a Stretched Blintzed Bird-Base--and made endless modifications to it, sacrificing purity of sequence for end-results (for we are no longer virgins). To list only the changes I am keeping: Off-centering the Bird-base, allows the tail to be made longer than the wings without additional folds. Off-centering the Blintz buys you all sorts of things. If you want to, you can have a model that’s fully rounded (I mean 360 x 360 degrees). I chose instead to use the extra material from the overlapping ‘blintz’ for various color-changes and also to design what is, at last, a reasonable lock, so the front stays in one piece (without wet-folding etc). Wing ornaments and so forth can be added optionally.




* * *

Simple as all this still is----it may not be simple enough. A standing bird has fundamentally four points, even when its wings are slightly split. A four-point model ought to designable reasonably from a bird-base. And if it’s a bird base, then the principle of continuous complexity ought to apply, and feet can be point-split if one cares to, a beak opened, and so forth, all from essentially the same beginnings, and stopping whenever one has had enough.

Can this be done?

Stay tuned.

P

Sink or Swim

The awful thing about this origami business is that it keeps changing. You can never rest on your laurels. At any given moment, somebody, somewhere is doing something mind-boggling, or worse, is busy outpacing you at the very thing you once most prided yourself in. I shudder to think what will happen if Ronald Koh ever comes out with a book—having seen a few of his Fish, the best in the world, and knowing something of the design problems involved: won’t a book will make it clear he’s one of the foremost animal designers of our time?

But there is no need for dreadful anticipations. As we speak, out there on the edge of the universe, in Calgary, Canada, Roman Diaz is plugging away at his Birds: carrying the study of avian origami to what I think everyone will recognize as new heights. His bird from the post before last (Nov 1 2006) is not so much a homage to Michael LaFosse’s Cardinal as a rival to it, in elegance of straight-line form and color (if not in simplicity of design), something I would scarcely have imagined possible. And in the ‘Calandria’ of the last post (Nov 9) there is more improvement still: this time on the rounded form of the bird. --All of which personally would be an unmitigated joy were it not for the fact I’d staked out some of this field for myself, once upon a time. I am not yet ready to cede at least partial ownership of it. Not without a fight anyway. I don’t mind losing but not quite so easily...

Let us pick nits. Roman says, if my feeble Spanish is getting it right: (a) very many birds in origami are indeed made from the Bird Base; and (b) without using High Technology, a standing bird with wings folded on its back will not show two distinct wings, but only one conjoined surface, if made from the Bird Base or any of the other traditional bases.

As to (a): I’m not at all sure this is factually true. We may have to consult the Origami Database (supposing it somewhere contains the useful category of bases a model was designed from) to see how many birds really are made from the Bird Base as a share of the total. The term itself certainly did not originate from any such preponderance of designs, any more than the ‘Fish Base’ is so called because most or even many fish derive from it (of that I’m surer: they don’t). Presumably only one bird ever gave rise to the term ‘Bird Base’—the Crane. Historians are of course invited to do their stuff here.




When I set out last year to show an assortment of ‘Bird-Based birds’ of my own design it was not because this seemed an especially natural or widespread thing for model-makers to do; the point was rather to show that there was life in this tired old base still, and that models of considerable purity and power can be made from familiar beginnings and relatively low technologies. (Dare to be ridiculously simple, stupid and obvious, my motto seems to be.) I was annoyed in particular by the birds Robert Lang had displayed at Barcelona (2005), which took over 50 steps to make; a few trials over the years had suggested that slightly simpler, but just as effective birds ought to be makeable in no more than 10 to 15 steps--or say 20 if you point-split feet, which isn’t always an improvement.

But having considered the matter further, it now seems to me that the Bird Base really is a natural beginning for birds, standing ones especially—even ones with substantial amounts of detail. That’s because it puts the points in all the right places and leaves them pretty much independent. If you want to add details that cost you limb length (e.g. point-split feet), you can always compensate by shortening the other elements proportionately (ideally adding detail there too). This then yields a design virtue I try to get from all of my own origami: something we may call ‘continuous-complexifyability.’ (Ugh. Ugh!) That is: a design should yield good enough results in its most simple format, but also be able to sustain gradual increments of complexity or detail, if that’s desired, without modifying the superstructure. The ideal would be for Roman’s useful ‘progression of bird complexity’ illustration to be the literal truth about adding details to the same model (or barring that, to the same concept). With a Bird Base, that is almost possible.

As to (b), the point about folded separate wings: As a generalization that may be true. But it also depends on what you consider to be the ‘Traditional Bases’ and what you take to be ‘High Technology’. (OK, so Roman did not use this term.)


For instance, here’s a picture of an actual 1987 model, the ‘Fat Pigeon’. It’s from a Stretched Blintzed Bird-Base. Does that count as a “traditional base? The technology is pretty ‘traditional’ too, i.e. practically obsolete, though in ‘87 it was state-of-the-art.

For the record, about six months ago I simplified this model (abandoning legs altogether) and made a version from a plain old stretched Bird Base. Here it is. This modification follows two design principles, the first one tried and true—“KISS”, or, ‘Keep It Simple, Stupid’—the second more theoretical and unproven: “POETIC”, or ‘Put Opposite Elements Together, Idiot, in Combinations.’ (yeah I just made this up.) Here the ‘combination’ is of 3D/rounded form with 2D and even 1-D elements--the paper’s cut edge, made visible.


And what about the Bird-Frog Base? That’s at least hybrid-traditional, and is getting more traditional by the minute. You can make a split-tail (not split wing) bird from it easily enough. I’ve also made a Whooping crane (1988) from it and, following the principle of continuous complexifyability (…), just adding toes, a Heron (2005). Its close cousin is the Crane designed by Daniel Naranjo and further developed by Roman Diaz himself—which is from a Waterbomb base, and so unquestionably “traditional”. The wings in all these cranes can be folded up in exactly the way actual cranes do it, creating a two-winged back, though for origami this would clearly be a waste.

But it’s true. If you add just the teensiest graft to a plain old bird base you can get away with a lot more. In particular you can not only get the wings on the back to split but send the tail shooting up between them, which in my lexicon of bird emoticons, is the very expression of Joy.

Thus far I’ve been discussing history, some of it ancient history. Hopefully next time I’ll have some new things to show.

So: am I holding my own? What do you think?

Folders of Columbia

Thanks for the terrific time you showed me the other week at the well-organized origami convention, and before that at the impressive mask exhibit and the LAO meeting. It is heartening to see how origami is flourishing and specially exciting to meet the design talent now emerging in your country.

I will remember your cities of Medellin and Cali---where the women have the most amazing figures; where (in Cali) at night in the rain, open-air busses go around with music blaring and people dancing on them, because those Columbians they can’t stop partying for a minute; and where (in Medellin) origami is taught at the University as a required subject …


Cheers

Saadya

"Expression" and "Idea" (part II)

There are different ways to engage and delight a viewer with something you’ve made, for instance, at the level of thought and at the level of feeling; but either way ‘engage’ usually means a mix of being clear and being obscure--both obscure and clear enough to make the viewer figure things out for himself and be able to reach the happy conclusion of recognition. With ‘model-making origami’ this happens almost automatically when the viewer recognizes simultaneously what the object is and that it is just paper with a few folds that the mind has figured out how to read. (So if the model is too detailed or if it is post-painted, we work less at translating it from paper-language and it gives less joy...) This would be a ‘cognitive’ ploy--it works at the level of thought, of recognition. But emotion comes into play in origami too, especially, it seems, with wet-folded models, for reasons I’m far from clear about.

A model can be stiff and cold and just say “this-is-a-that”, but it can also DO stuff and so engage the imagination in other ways. Think of the object as being like a noun: it can fit in lots of different sentences, or stories, but maybe there is not enough there to invite the imagination of them (unless you are a child). Well-made sculpture, as Roman points out in his comment, does not leave the thing to float entirely free, declaring just ‘X’, but often adds a bit of carefully-chosen adjective or verb to the noun (goat grazing, bird perching). When done right the posture or action seems as though it is about to change. That’s part of what gives the thing ‘life’: it has its own autonomy, a freedom of choice your imagination has granted it, to move beyond what is actually represented. When this succeeds, the object and you are bound up in a story-making relationship. (It is ‘interactive’, even if the wings don't move when you pull its tail.) And when the object is origami, and you're the one who has folded it, the imagination-space has been widened by a background of creation or parentage as well as by a link with the mind of the designer. A history of guided moves, along with the choices made and unmade. (Thanks Roman for helping me think this through.)

If the object is composed of several main parts, then you have a ‘sentence’ with more of the elements filled in: A is doing B to C (or stands in relation B to C). If the two parts are of equal weight, you tend to notice the verb more than the nouns—the sculpture is about the relationship. With more than two parts you are starting to control a whole story, with a protagonist to be identified with, subordinate clauses, a background scene etc. In my experience such sculptures tend to function more in painting mode than in sculpture mode; that is, they are sometimes less physically ‘present’, maybe because there is less freedom for the parts or the whole to do something other than what they are doing. Somebody is telling you a tale, the objects are not confronting you freely or directly and of their own accord. (Mobiles are an exception that proves the rule.) --Sentences or stories exist in a different space than objects do. But even with stories the obligation remains of engaging the viewer’s imagination—by obscurity or by every other trick that will serve. And so you introduce, for instance, suspense.

This is taking us a bit far afield. I wanted to focus here on the work of one great 'conceptual ' explorer, who has something to say about pure model-making (the naked noun, stripped of all verbiage) and also about the nature of paper itself.

He is of course Herman Van Goubergen. I will not be speaking here about all of his work, only the theme in it of the two-sidedness of paper. (Another theme is the difference between flatness and three-dimensionality, but we have already been stressing that quite a bit in this blog.)


Three models of his come to mind. First (1988?), there was his Lion-with-color-change. Now, color-changes are not uncommon in origami, today anyway, and if one is looking for pioneers here one certainly will think of Neal Elias before Herman Van Goubergen. But what strikes me with this model is that the color-change potential of paper is not just being used, it is being called attention to. The subject of this model is as much ‘The Color-Change’ as it is ‘The Lion’. I am not entirely sure how this is effected. Maybe it is because in the front of the model the color change comes out so cleanly at the right places and nowhere else; or maybe it’s because at the rear, exactly where the model is ‘anatomically correct’ it is also ‘color-change incorrect’. Attention is naturally drawn to that part of the anatomy anyway and when a further visual cue is added you become aware that both nature and art are engaging in some extra signaling—all of which stimulates thought. (Thought, I insist, more than feeling: cold idea more than warm expression.)

The next model in this progression is ‘Above the Water, Under the Water’ (1996?): a model is posed on a glass ledge over a mirror; viewed from above you see a bird, but in the reflection from underneath you see a fish. —When I first encountered this model in Salzburg last year I immediately thought of M. C. Escher, who likewise was specially enamored of birds that turn into fish and with the idea that the same thing looked at from a different perspective can be a different thing. (Escher even has some prints in which you look at a puddle of water, see things reflected in it, floating on it and submerged in it: above, on and under). I pointed out these possible connections to Van Goubergen, an iconoclast and original thinker if ever there was one, and he seemed none too thrilled about them.

This model is using not just the color change but also the fact that an origami model almost always ends up with a top and a bottom (or a front and a back), and that it is by convention only that we attend to the top in mentally constructing a model out of what we see, while disregarding the messy underside. Once again Van Goubergen is calling attention to a fact about paper and paperfolds—or about ourselves. When other designers, most notably Joisel, find the two-sidedness of 3-D models objectionable they quite sensibly apply their immense ingenuity to hide or to eliminate it; Van Goubergen makes use of this property and so forces us to consider it.

Nice and subversive.


But the apex of this progression has to be that VERY strange Skull of his (diagrams in the Origami USA 1999 convention book and in Origami Tanteidan #72). A shape, not immediately recognizable, is placed on a mirror: now the reflected underside combines visually with the directly-seen top, and it becomes a skull. Brilliant! The color-change aspect has been done away with, the idea has been purified. It is now only about tops and bottoms. The model’s normally-ignorable underside can’t be ignored at all, because without it we don’t so much as have a visually constructible object. Bottom and top are of equal importance and neither is sufficient by itself for a unified model. Fantastic.

By the way: this sort of optical trick has not, so far as I know, ever been done before and it is something of an honor for us in origami that it was done in paperfolds first.

If you ask, technically, what the connection is between the idea of the color change and the top-and-bottom aspects of origami models, it is this. Paper starts out with two sides, which may be bi-colored; but while you can quickly hide the color (e.g., by a blintz) the result will still have two sides. The two-sidedness of the developing model continues essentially through all stages in which it is folded flat. Since three-dimensionality is usually given only at the very last stage, the model typically retains a top and a bottom, or an outside and an inside plus a seam-line, the latter of which we have no choice but to ignore.

This then is an ‘expression of an artistic idea’, in at least the following respects. It is an idea about paper, or paperfolds; about the mental construction that parallels the physical construction of origami; about redeeming the ignored; about one thing that really always was two and two things that again become one.


Isn’t that a lot of 'idea' to pack into a single square of paper?



Saadya

"Expression" and "Idea" in Origami

Just a few years ago I read some words—either by John Smith or David Lister: one of the ones who can write—to the effect that it’s unlikely origami will ever be used as a means of ‘expressing artistic ideas’. Just what the author thought was impossible or unlikely may not have been precisely spelled out, but it's always been clear that origami imposes severe constraints on creation so that it’s not the first medium you think of if what you are after is self-expression.

Even so, it’s always dangerous to prognosticate, and the boundaries of ‘expression’ and ‘idea’ are being pushed back these days too as part of origami’s general advance-on-all-fronts.

It seems to me that there are several different concepts embraced by these terms, and that it may be worth unpacking them a little.


I. There was and still is an old-fashioned sense of expressiveness in animal origami which was for a long time associated with the name of Yoshizawa, though he’s acquired quite a few heirs and rivals by now. I think everyone knows what this quality is or reacts immediately and strongly when faced with it; but it is still very hard to pin down in words. Is ‘expression’ the capturing of a particular species in its essential details? Maybe; though sometimes the representation is very abstract or minimal, and that is thought sufficient or even preferable. Is it the capturing of an emotion expressed by an animal? One of its typical gestures? Or perhaps it is eliciting a particular kind of emotion or expression on the part of the viewer?

In the end one resorts to some words that sound about right. These great designers and folders were somehow able to capture the soul of the animal or the thing, and to breath life into a sheet of paper. Just what this animation or ensoulment is, in a day and age when we’re not supposed to believe in souls, has never been properly articulated. Maybe it can’t be. Still, ‘soul’ seems about the right word here: the object before us is haunting and absorbs all attention; in a few crisp folds it concisely yields the animal’s essence; and it has a light, delightful, ephemeral presence—all things a soul is supposed to be or to do. --Readers of this Blog will be aware, too, of my prejudice that origami has special abilities in the ensoulment department, gifts not readily accessible to the other arts.

If origami animals can express souls—what about origami humans: can’t they have souls? Strangely, this has proven far more difficult. Some not insubstantial progress for expressiveness has been made of late for human faces, but figures, or heads attached to their bodies, have proven much more recalcitrant to paperfolding—and not, it seems, for technical reasons. Technically, it is no harder to make a stick-figure human being, using the logic on which Lang’s Treemaker software is based, than it is for any other animal. Likewise, box-pleating methods have long been available and indeed have been used for humans too. But artistically—with apologies to the many laborers in this field—very few of the (unclothed) humans made via these methods have come anywhere near to being satisfying.

Consider, for instance, Stefan Weber’s glorious Bulls, the centerpiece of the Red-Bull-sponsored Masters of Origami exhibit last year in Salzburg. One can now go home and sleep comfortably knowing that the Soul of the Bull has been done justice to. It no longer hangs in Origami Purgatory. Can the same be said for any human figure you can think of—even by any of the greats, by those same ‘Origami Masters’?

I have, needless to say, strong suspicions about why this is—about which of the directions people are moving in today are dead-ends, and which lines of attack show real promise. But maybe I ought to keep a few secrets for myself.

2. So this is one category of ‘expressiveness’. Another involves ‘expressing artistic ideas’. This is a little like what Conceptual Art does. Here the aim is less to surround a lone sculpture with a halo of attention or emotion or expressiveness—investing it with objecthood—but instead to convey an idea or a mini-story, usually by relating one part of the image or object to another, perhaps as contrast or irony. A terrific example in paper is the work of Peter Callesen, which has been making the rounds of the Internet lately. If you haven’t seen it, it’s worth quickly running through this show to see some of the possibilities and logic of the ‘conceptual’ approach.

This is of course not origami—it is all about cutting paper, so is a kind of opposite to paperfolding. But it is allied to origami in the strictness of its rules, in the economy of the material, and, of course, in its use of paper-folding. The main rules seem to be that what gets to there must come from here, honestly, visibly and meaningfully; and that the cut out part must still be connected to where it came from, usually physically but sometimes just conceptually. (These rules are 'discoverable' rather than spelled out in advance as in origami, but they are always there, and the sense of limits or fate and morbidity is among the themes Callesen plays off so marvelously.)

Much more can be said about this line of art but all I want from it at the moment, is to suggest that to get to a ‘concept’ (especially if irony is involved), maybe you need the object to have several distinct parts which relate — or pose a question of the relation — between them. To get to a ‘story’ you need the parts or the whole to suggest an order in time, something that has happened or is about to happen. In Callesen’s work there are always three parts (counting the background material); there is also always an implied history of how the thing came to be the way it is. These together give a halo of idea and story almost automatically (though before Callesen introduced and relentlessly explored this possibility in paper-cuts, it seems not to have been quite so obvious).

Now origami, which by its nature puts more stress on contiguity and wholeness, tends not to investigate this kind of 'expression' and lingers more on the model-making side of things, the this-is-a-THAT. And in model-making, the artistic possibilities seem to consist of accuracy of representation, or conversely abstraction and minimalism, and sometimes ‘emotion’ or ‘expressiveness’. Yet it does not follow that either the 'story' or the 'concept' side of art-making is ruled out of origami altogether. In my next post I want to discuss two designers who do, in fact, explore this ‘conceptual’ potential in paperfolds.

Lessons from Masters

This was the image that stopped me dead in my tracks, about two years ago.

It is a stone Buddha, from the 3rd century, made in North India: artist unknown. I don’t remember anywhere having seen such repose, or balance, in a sculpture or a living face; this degree of simultaneous worldliness and withdrawal-from-the-world. (To meet it, be its equal: not to resign from it!). Actually I know nothing of Buddhism, and intend not to learn. But this one head—well it ranks in my book as one of the world’s great sculptures, of which there are very, very few.


Since, at the time, I was beginning to explore methods of making faces in paper, needless to say I tried to copy this head. And needless to say I failed. But the effort did spawn a series of ‘Buddha-like’ origami heads, in which something ancient and Eastern came out, maybe by way of minimalism, simplicity, modesty and humor; and maybe by using properties of paper not available to those who work in stone (a warmth, vulnerability, fragility). Here are two of the things I have in mind from then:





Now emotion, expression, are the most important things in whatever one sees, and the most obvious. But it’s no secret that origami combines its ‘art’ with its ‘science’, its expression with its intellection, more or more manifestly than any visual art I can think of. That’s one reason I’m drawn to it. Without making too much of this, origami, though it’s mostly an addiction, is also a world-view: it has its ‘Zen’. It calls forth and then pits the various human skills against each other: like a boxing match, where half the thrill is wondering which quality will win out, brute force and rage against careful training and intellect; ‘heart’ or stamina against spikes in power; an ability to take punishment against the ability to inflict it. So in origami, there is clearly technical control, engineering skill, representational accuracy, the kind of mastery that can squeeze a flap from any bit of real estate; but these are pitted against the artistic virtues: simplicity, heart, elegance, rhythm, economy, expression. Which will prevail? The contest is not less suspenseful for the square sheet of paper than it is in the square arena of the boxing ring.

Since there is technique and ‘science’ in our worldview, let us look again at that stone Buddha from the 3d century. What can be learned from it about folding technique—specifically, now, about folding curves in paper?

Look closely: you’ll see that all the lines in this sculpture are curved. But more than this: none of the curves intersect! You’ll either see ovals, that is, lines that are continuous and endless, or curves that end by meeting other curves—but at a tangent, at an angle of zero, so that these lines too are continuous. Where curves terminate altogether they die out softly into the plane.

Astonishing, no?

It is clear that the artist has gone out of his way to get this result. I’m no expert on Eastern sculpture, so I don’t know if this was an innovation achieved first in this particular work or if it is part of a wider trend; but there is no doubt that the technique contributes to this sculpture’s sense of repose. And no doubt, either, that it is giving a visual expression to essentially religious ideas about the flow of life, concord rather than discord, continuity, eternity etc.

For paperfolding--why does this matter?

A question that keeps coming up from various quarters, is Whether anything you do with a curved line can’t be done roughly comparably with a straight line (or straight segments). For instance: If your pattern uses a sine curve, couldn’t you just as well have used a zig-zag? Are curved folds special in any way?




Here is a crease-pattern for the famous Huffman Tower, and a folded version. Could all the curved folds and curving surfaces here have been replaced by straight lines and flat planes? (Try it and see.)

This question about straights and curves comes up in part because some of our more technically or computationally-minded origami people seem to regard curved folds or surfaces as essentially bi-products of straight-line folds (instead of what would seem the more natural view—to consider straight lines and flat surfaces as curves with a few extra properties). One wonders, accordingly, whether this is just a fixation on the part of these designers or whether there is any basis to their approach.

The question also comes up because there are all sorts of claims in the air nowadays about the specialness of certain curved folds or their effects; for instance, about locks that are only possible with curved folds, models ‘held in tension’ by them, special surface topologies induced by them, etc. Some of these claims are true and others false; but many, it seems to me, are simply untested. Having straight-line analogs gives a means of testing in a given case whether it’s really the curvature that’s doing the work, and that’s an important reality check.

Anyway—to return to the inspiration from the Buddha—there’s at least one thing you can do with curves that you can’t do with straight-line segments: get two of them to meet at a tangent. A straight-segment’s tangent is itself; the points at its termini have no tangent. Curves, on the other hand, have no problem meeting either straights or other curves at a tangent. This is actually quite significant if you are folding surfaces containing open folds (folds resulting in surfaces that do not lay on each other).



In the drawing shown here (a CP of open-folds and curves), after you’ve made the more ‘horizontal’ open folds and thus have condensed the vertical direction somewhat, you are not free to fold the surface along [A] without making a real mess--lots of new folds in awkward and unpredictable places. (This is the corrugation effect.) However, since all the horizontal lines in this region are straight, you can turn them into fully closed folds—and then line [A] can be folded. Along [B], where the zags zig, you can comfortably fold the surface without introducing any new folds. The corrugation no longer provides a resistance. Folding it here will, however, further condense the height of the surface, as the angles intersecting with [B] give up some of their height for depth.

Along the line of [C], the surface will not fold—just as it couldn’t at [A]; but if the entire region of [C] is turned into a gradually curving corner, that region will behave just as the zig-zag at [B] does (in fact it is a blown-up version of it), and then the height will likewise shrink.

Folding along [D], however, will not affect the height of the surface at all: that’s because the curves meet [D] at a tangent, so they don’t interfere with it. (However, as the material to the left and right of D condenses, it will force D to bend along the point of contact.)

So here you have one difference between curved and straight-segment folding: the non-interference of tangential folds. And this principle happens to affect nearly everything about the possibilities of folding surfaces that have curved folds on them.

This is not a religious insight, or even a profound or novel mathematical one. But it might give a few people who are thinking now about sculpting in paper curves----a certain repose.

Curves vs. Flats

Origami, like anything with a long history, also has a destiny; by which I mean for instance that folds that were thought to be extremely difficult 100 years ago are child’s play today, and forms that 60 or 70 years ago were thought to be impossible without making cuts—so that a cut here & there was overlooked—are known as perfectly possible today with a little extra effort. Cuts accordingly are more strictly shunned even by non-puritans. The preference for the square has grown firmer, though it’s by no means absolute; and the field has grown enough to allow modulars, multi-part assemblages, though this is frowned upon in animal design (unless the units are sufficiently small to make it an extension of modular origami.) In short, the field has naturally pushed toward a set of ideals or strictures, which on approach have sometimes further split into other ideals and strictures each of which defines a new sub-field. Moreover, one can claim that this ‘destiny’ was present if dimly felt by some practitioners in earlier stages of development, and the very refinement and purification of such standards is part of what drove those pioneers forward.

Curved folding, a subspecies of origami, has not been systematically explored by anything like as many people. (I’d say less than twenty people in the world; maybe less than ten, compared to several hundred systematic explorers with origami.) But I insist that curved folding too has a destiny---and I’ll tell you what it is. If in origami you rule out (or minimize) cutting, painting and gluing, in curvigami you also rule out folding itself. That is: hard folds and straight lines are viewed as necessary evils, acceptable in extremis, in just the way cuts were regarded in the origami of two or three generations ago.

What about the square—another purist ideal that’s been refined (I mean increasingly insisted upon) over the generations? Here there is a more profound difference from straight-line and flat folding. Curvigami deals with surfaces and starts from the interior of the sheet, asking how you can manipulate that interior and what to do with the consequences of this manipulation for the rest of the sheet. This is unlike origami, which deals with edges, or the turning of surface regions into things that have edges, i.e., flaps. With curved folding you are dropped straight into the sea, where what you make are these ripples or waves; there is no shoreline you can depend on, and no “landmarks” either (I can go on some ways with this metaphor). So that the square with its edges and its whole language of 22.5 degree or 30 degree angles really becomes irrelevant. If you’re manipulating the edges and the corners of a square you are still more in origami mode than in curvigami mode.(Though this can be done masterfully too: witness Roman Diaz’ superb Tiger’s Head). I feel regrets about the loss of the square, truly I do, but it must go.

That being said, I can’t quite account for the residual attachment to the rectangle in my own curved folding, and to the right angle at its four corners. –Maybe it’s that one wants to keep it clear that a sheet, and a paper sheet, is the material of origin here, and sheets are rectangular by manufacturing tradition. Or maybe it’s that representation-surfaces in general—for instance paintings, and then movie and TV screens and now computer and cellphone screens—have historically allowed only very occasional lapses into other shapes: ovals, triangles, pentagons etc. It is the rectangle that silently screams today ‘surface’—or ‘surface without shape’, or ‘never mind about the edges or proportions, which within limits we can vary, it’s the interior content that counts’. That ‘surface condition’ exists also for surfaces to be made into curved-folds. A square, or any other regular polygon, draws far too much attention to its own outline and geometry.

Since curved folding is about surfaces, layers, too—the staple and mainstay of origami—also are downgraded. Layers are not mined as in origami for the creation of different entities (usually flaps); instead, multiple layers (which are avoided or minimized to begin with) are often treated as thicker versions of a single layer, and are folded all together.

To me, the great still-unanswered question is what the area of contact is between flat folding and curved folding. You might think, that since curved folding deals with surfaces, you can use curves for placing a surface ornamentation on an elaborate form, in, say, the way Robert Lang does famously with his Koi. But if the curves are put in first they prevent most subsequent manipulation of the familiar kind, so such an elaborate form is ruled out. Nor is it usually easy to put curves in after the fact, unless there is free material that reaches all the way to the cut edge. Roman Diaz’ Tiger’s Head (looks like I’ll have to write a separate essay on this model alone) introduces a few ornamental curves on the ‘leftover’ flat regions as a final step. This is not QUITE an afterthought, what it feels like instead is pedagogy: we’re being taught something about sculptural folding, in the rest of the piece, and here is an important aspect of sculpting that we don’t want to omit or the lesson won’t be complete. Nevertheless, the curves were not strictly necessary, some straight open crimps could almost have served. And the curves would not really have been possible, if the cut edge had not been free. --In some of my own things (e.g. Ernestine [yes, it's time for some new examples]), the ‘combination’ of curving/sculpted regions with flat/origami ones is given as a sort of ‘tease’, with the single-layer-curved head blending into the face (which has a few origami manipulations, I mean layers and flaps) and that in turn blending into the neck and chest, which is even more oriented to the language of straight-line origami. The suggestion--meant as usual to irritate certain people--is that the curves and the sculpting are the main thing, with the flat and straight origami being subservient to it, the raw material that it grows out of, in the way a polished marble sculpture can emerge from unthinking chiseled stone. Something similar about the relationship was suggested more humorously in ‘The Origami Eater’. But I haven’t given up the idea of curves as ornaments either; that’s part of what I was looking at in those ‘jars’, where a curve-pattern is carried around an edge; the n-sided jar-shape being the origami superstructure which supports the curving bas-relief ornament. Here the curved/sculpted regions and the geometric/origami regions are felt to be on more of an equal footing.

Why this fight over primacy, subservience etc? Must the elements of one language always be reduced to those of another? Can’t we all get along?

But looks like I’ve run out of space, or is it time. Let's leave this question open--for the time being.

[Added later: A slightly more formal discussion of curve-folding issues appears in the next article, "Lessons from Masters".]